12.09.2005 H. Stockhorst

Cooling Scenario for the HESR

HESR Layout

Electron Cooling at Momenta p ≤ 8.9 GeV/c

for the High Resolution Mode

Small Angle and Energy Scattering

Stochastic Cooling with Internal Target

for p ≥ 3.9 GeV/c in the High Luminosity Mode

COOL 05, Eagle Ridge, Galena, IL USASeptember 18th to 23th, 2005

H. StockhorstForschungszentrum Jülich GmbH

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HESR Layout

Circumference: 574 m Arc Length: 155 m Straight Section: 132 m

Ions: - anti-protons - protons

Momentum Range: 1.5 GeV/c – 15 GeV/c

anti-proton injection

at 3.9 GeV/c from RESR

Basic Parameters:

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Scenario High Resolution Mode

The beam is injected into HESR at T = 3 GeV

Electron Pre-Cooling

Acceleration to the Desired Energy

Electron Cooling and Target ON

Luminosity L = 2 ⋅ 1031 cm-2 s-1

Number of Anti-Protons N = 1010

Target Area Density NT = 4 ⋅ 1015 atoms/cm2

rms-relative momentum spread ≈ 1 x 10-5

required up to 8.9 GeV/c

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Cooling Models Simulation with BETACOOL

Model Beam Option

Semi Empirical Formula by V.V. Parkhomchuk

" rms-Beam Option

"Transverse Cooling:Model by B. Autin

"Longitudinal Filter Cooling:T. Katayama and N. Tokuda (and H.St.)

Electron Cooling Stochastic Cooling

HESR Lattice with γtr = 6.5i

Intra Beam Scattering (IBS): Martini Model

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Electron Cooler Parameters

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Electron Cooling at T = 3 GeV

Final relative rms-momentum spread: 3.4 x 10-5

• The equilibrium is determined by IBS

• The target is switched on at about 22 s. No influence

target ON

red: horizontalblue: vertical rms-emittances

rms relative momentum spread

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Time Evolution of the Momentum Distribution @ 3 GeV

beam distribution

• Initially: dense core and long tails

• At equilibrium: Gaussian distribution

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Electron Cooling at 8 GeV

cooling OFF • Electron cooling and target ON

• Equilibrium dominated by IBS

rms-momentum spread with target and IBS : 3.0 x 10-5

red: horizontalblue: vertical

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Resume

The High Resolution Mode with δrms ≈ 3.0 x 10-5 up

to T ≈ 8 GeV seems possible with electron cooling.

But

No phase space distortion during acceleration has

been assumed.

No phase space increase during injection

In the HESR Synchrotron Mode:

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Scenario High Luminosity Mode

The beam is injected at 3.9 GeV/c

Acceleration to the desired momentum

Stochastic Cooling

to compensate target-beam heating

Luminosity L = 2 ⋅ 1032 cm-2 s-1

Number of Anti-Protons N = 1011

Target Area Density NT = 4 ⋅ 1015 atoms/cm2

Required in the whole momentum range

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Small Angle and Energy Loss Stragglingfor the High Luminosity Mode

F. Hinterberger, INTAS Workshop, 3.6.05, GSI

• Introduce scrapers to limit the maximum relative momentum deviation by δCut = 10-3 will decrease the squared rms deviation per target traversal by more than one magnitude above T = 8 GeV.

• The relative particle loss rate is less than 15 %/h above T = 8 GeV.

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Small Angle and Energy Loss Straggling

• small angle scattering is less important above T = 8 GeV.

• the maximum emittance increase is about a factor of two over one hour at T = 8 GeV.

• Dominant process: Increase in momentum spread above 8 GeV

(DC-beam)

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Transverse stochastic cooling seems to be only necessary below 8.9 GeV/c.

Longitudinal stochastic cooling is necessary in the whole range.

Scenario High Luminosity Mode

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Longitudinal Equilibrium with Stochastic Cooling and Target

Longitudinal filter cooling for a Gaussian distribution obeys the differential equation

Schottky noise heating

N: particle number, nP,nK: number of PU, KI loops, W: bandwidth,fC: center frequency, GA: electronic gain, 2/τ: cooling rate

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Longitudinal Equilibrium with Stochastic Cooling and Target

Schottky noise equilibrium: Target equilibrium:

equilibrium relative rms-momentum spread:

N: particle number, nP,nK: number of PU, KI loops, W: bandwidth,fC: center frequency, GA: electronic gain, 2/τ: cooling rate

with contribution from

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Longitudinal Equilibrium with Stochastic Cooling and Target

For a given bandwidth W and center frequency fC of the cooling system as well as particle number N the minimal equilibrium value is attained for a certain value of the product ( nP nK ) 1/2 GA.

The number of pickup loops nP, the number of kicker loops nK and the electronic gain GA can be chosen to optimize the signal-to-noise ratio at the pickup output and to keep the electronic power in reasonable limits.

The only way to reduce the equilibrium value (and cooling down time) for a given particle number N is to increase the bandwith W and the center frequency fC .

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(2 – 4) GHz System Quarter wave loop pairs for pickup and kicker: #64 Electrode length and width: 2.5 cm Gap height: 2.6 cm Pickup/kicker length ≈ 3 m Beta function at pickup and kicker: 75 m Impedance: 50 Ohms Cooled structures and eq. amplifier temperature (both 80 K)Longitudinal cooling: Optical notch filter

Transverse cooling: Pickup/kicker in difference mode

Low electronic power < 200 W

Below T = 3 GeV longitudinal band overlap

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Longitudinal Stochastic Cooling Performance for Different Momenta in the HL mode

Transverseand Longitudinal Cooling

Including IBS+Target

p = 3.9 GeV/c

L = 2 ⋅ 1032 cm-2 s-1

N = 1011

NT = 4 ⋅ 1015 atoms/cm2

red: horizontalblue: vertical rms-emittances

rms relative momentum spread

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Longitudinal Stochastic Cooling Performance for Different Momenta in the HL mode

L = 2 ⋅ 1032 cm-2 s-1

N = 1011

NT = 4 ⋅ 1015 atoms/cm2

above 8.9 GeV/c only longitudinal cooling

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Stochastic Cooling Performance for Different Momenta

For all energies above T = 3 GeV almost the same equilibrium relative momentum spread values are attained.

Target heating can be compensated.

As compared to electron cooling: IBS plays (almost) no roleif the beam is only longitudinally cooled.

If the momentum aperture is limited to

δCut = 2 ⋅ 10-3 the rms relative momentum spread can be cooled down by more than a factor of two.

Below T = 8 GeV transverse cooling is needed and can be achieved with the (2 – 4) GHz system.

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References• D. Möhl et al., Phys. Rep. Vol. 58, No.2, Feb. 1980 • Design Report Tevatron 1 Project, Sept. 1984, FNAL

• B. Autin, IEEE Transactions on Nucl. Science, Vol. NS-30, p. 2

• B. Autin, ”Fast Betatron Cooling in an Antiproton Accumulator”, CERN/PS-AA/82-20

• F. Hinterberger and D. Prasuhn, Nucl. Instr. and Meth. A279(1989)413

• T. Katayama and N. Tokuda, Part. Acc., 1987, Vol. 21 according to a private communication with Tokuda the noise contributions have been recalculated by H.St.

• A.Smirnov, A.Sidorin, G.Trubnikov, JINR, Description of software for BETACOOL program based on BOLIDE interface

Thank You for Your Attention